Question

Thermal conductivity of a metal rod depends on:
(A) Area of cross section
(B) Temperature gradient
(C) Time of flow of heat
(D) None of these

Answer 1

First let us see what is meant by thermal conductivity:
Thermal conductivity can be characterized as the rate at which heat is moved by conduction through a unit cross-segment area of a material, when a temperature inclination exists opposite to the area. The reciprocal of thermal conductivity is known as thermal resistivity.

Complete step by step answer:
Fourier’s thermal conductivity law (also known as the law of thermal conductivity) specifies that the rate at which the heat is transmitted through the material is proportional to the negative temperature gradient and is also proportional to the region through which the heat flows.
Mathematically this law is expressed as:
$q = - k.\nabla T$
Where $\nabla T$ refers to the temperature gradient, $q$ denotes the thermal flux or heat flux and $k$ refers to the thermal conductivity of the material.
Mathematically thermal conductivity is given by:
$K = \dfrac{{QL}} {{A\Delta T}}$
Where $K$ is the thermal conductivity, $Q$ is the amount of heat transferred, $L$ is the distance between the two isothermal planes, $A$ is the area of the surface and $\Delta T$ is the difference in temperature.
Thermal conductivity is a material property. It doesn't rely upon the temperature change. Thermal conductivity is dictated by whether the material is translucent or non glasslike, kind of molecules that make up the strong, their vibrational character, bond quality, bond type, and so forth.

From the above discussion it can be assumed that thermal conductivity does not directly depend on any of the given options. Hence, option D is correct.

Note: Although thermal conductivity does not directly depend on temperature. The heat flow is dependent on the temperature gradient. The metal surfaces tend to expand when temperature is increased.